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Unformatted text preview: Fall 2010 Optimization I (ORIE 3300/5300) Assignment 7 Solution Problem 1: AMPL 4-3 (a) The marginal values associated with the constraints Time[t] are: ampl: display Time; Time [*] := 1 2660 2 3080 3 3400 4 3400 Therefore, additional production capacity would be most valuable in periods 3 and 4. (b) ampl: display Sell.rc; Sell.rc := bands 1 1.7 bands 2 0.6 bands 3 bands 4 coils 1 coils 2 2 coils 3 1.71429 coils 4 3.71429 Because the sum of the reduced costs for coils is greater than for bands, we should go after more orders of coils each week in order to make the largest possible improvement in profit. (c) We will only produce what can be sold at some point in the planning horizon since the value of leftover units at time T is zero. If there were inventory in period T, we would simply throw away these goods, but we would have incurred a production cost. This would contradict any profit-maximizing policy that ends at time T. Therefore, any optimal policy will have and ending inventory of zero. In addition to the extended-horizon modification proposed in the problem, we could add a constraint that requires an ending inventory in order to mitigate the end-effects Grading scheme: Part a) was worth 3 points. Part b) was worth 3 points. No credit was lost for misinterpreting the question as asking for a single preference across all 4 weeks as opposed to a preference for each week. In part c) the explanation of why there should be 0 inventory at the end of the time period was worth 2 points. A proposed change to the model to circumvent the end effect was worth 2 points....
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This note was uploaded on 11/11/2010 for the course ORIE 3300 at Cornell University (Engineering School).